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Robotic packaging using wrapping paper poses significant challenges due to the material's complex deformation properties. The packaging process itself involves multiple steps, primarily categorized as folding the paper or creating creases.…
It is commonly believed that the most efficient way to pack a finite number of equal-sized spheres is by arranging them tightly in a cluster. However, mathematicians have conjectured that a linear arrangement may actually result in the…
Granular matter takes many paths to pack. Gentle compression, compaction or repetitive tapping can happen in natural and industrial processes. The path influences the packing microstructure, and thus macroscale properties, particularly for…
We describe a new numerical procedure for generating dense packings of disks and spheres inside various geometric shapes. We believe that in some of the smaller cases, these packings are in fact optimal. When applied to the previously…
Random packings of objects of a particular shape are ubiquitous in science and engineering. However, such jammed matter states have eluded any systematic theoretical treatment due to the strong positional and orientational correlations…
The problem of packing ellipsoids of different sizes and shapes into an ellipsoidal container so as to minimize a measure of overlap between ellipsoids is considered. A bilevel optimization formulation is given, together with an algorithm…
In the Colored Bin Packing problem a set of items with varying weights and colors must be packed into bins of uniform weight limit such that no two items of the same color may be packed adjacently within a bin. We solve this problem for the…
We study the generalized multidimensional bin packing problem (GVBP) that generalizes both geometric packing and vector packing. Here, we are given $n$ rectangular items where the $i^{\textrm{th}}$ item has width $w(i)$, height $h(i)$, and…
We extend our theory of amorphous packings of hard spheres to binary mixtures and more generally to multicomponent systems. The theory is based on the assumption that amorphous packings produced by typical experimental or numerical…
Gravity inversion allows us to constrain the interior mass distribution of a planetary body using the observed shape, rotation, and gravity. Traditionally, techniques developed for gravity inversion can be divided into Monte Carlo methods,…
We theoretically study the behavior of vesicles filled with a liquid of higher density than the surrounding medium, a technique frequently used in experiments. In the presence of gravity, these vesicles sink to the bottom of the container,…
Although the concept of random close packing with an almost universal packing fraction of ~ 0.64 for hard spheres was introduced more than half a century ago, there are still ongoing debates. The main difficulty in searching the densest…
Functional soft materials, comprising colloidal and molecular building blocks that self-organize into complex structures as a result of their tunable interactions, enable a wide array of technological applications. Inverse methods provide…
Dense packing of particles has provided important models to study the structure of matter in various systems such as liquid, glassy and crystalline phase, etc. The simplest sphere packing models are able to represent and capture salient…
We study the optimal packing of short, hard spherocylinders confined to lie tangential to a spherical surface, using simulated annealing and molecular dynamics simulations. For clusters of up to twelve particles, we map out the changes in…
The convex shape contained in a disk having prescribed area and maximal perimeter is completely characterized in terms of the area fraction. The solution is always a polygon having all but one sides equal. The lengths of the sides are…
This paper proves a bottom-left placement theorem for the rectangle packing problem, stating that if it is possible to orthogonally place n arbitrarily given rectangles into a rectangular container without overlapping, then we can achieve a…
We study packings of bidispersed spherical particles on a spherical surface. The presence of curvature necessitates defects even for monodispersed particles; bidispersity either leads to a more disordered packing for nearly equal radii, or…
We examine the optical properties of a system of nano and micro particles of varying size, shape, and material (including metals and dielectrics, and sub-wavelength and super-wavelength regimes). Training data is generated by numerically…
Iterative rounding has enjoyed tremendous success in elegantly resolving open questions regarding the approximability of problems dominated by covering constraints. Although iterative rounding methods have been applied to packing problems,…