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This paper describes a numerical method for finding good packings in Grassmannian manifolds equipped with various metrics. This investigation also encompasses packing in projective spaces. In each case, producing a good packing is…
Inverse design, where we seek to design input variables in order to optimize an underlying objective function, is an important problem that arises across fields such as mechanical engineering to aerospace engineering. Inverse design is…
3D shape completion is traditionally solved using supervised training or by distribution learning on complete shape examples. Recently self-supervised learning approaches that do not require any complete 3D shape examples have gained more…
The design of fusion devices is typically based on computationally expensive simulations. This can be alleviated using high aspect ratio models that employ a reduced number of free parameters, especially in the case of stellarator…
The densest local packings of N identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained using a nonlinear programming method operating in conjunction with a stochastic search of…
Inverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the…
Disordered metamaterials are promising for programming physical properties across diverse applications, yet their inverse design remains challenging due to the non-intuitive structure-property relationships and large design spaces. Recent…
Rigid particles pack into structures, such as sand dunes on the beach, whose overall stability is determined by the average number of contacts between particles. However, when packing spatially extended objects with flexible shapes,…
The structure of the densest crystal packings is determined for a variety of concave shapes in 2D constructed by the overlap of two or three disks. The maximum contact number per particle pair is defined and proposed as a useful means of…
Packings of hard polyhedra have been studied for centuries due to their mathematical aesthetic and more recently for their applications in fields such as nanoscience, granular and colloidal matter, and biology. In all these fields, particle…
Combining experimental procedures and theoretical modeling, we studied patterns, shapes, and growth of a special type of SuperAbsorbent Polymers (SAP). At the initial stage, embed in water, we have a polygonal pattern over a spherical form,…
Dense hard-particle packings are intimately related to the structure of low-temperature phases of matter and are useful models of heterogeneous materials and granular media. Most studies of the densest packings in three dimensions have…
The problem of packing a set of circles into the smallest surrounding container is considered. This problem arises in different application areas such as automobile, textile, food, and chemical industries. The so-called circle packing…
In programmable matter, we consider a large number of tiny, primitive computational entities called particles that run distributed algorithms to control global properties of the particle structure. Shape formation problems, where the…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
We report numerical investigations of a three-dimensional model of diffusive growth of fine particles, the internal structure of which corresponds to different crystal lattices. A growing cluster (particle) is immersed in, and exchanges…
A novel effect in a granular material under swirling motion of the container is presented. At low packing densities the material rotates in the same direction as the swirling motion of the container (rotation). At higher densities the…
Molecular simulations of the self-assembly of cone-shaped particles with specific, attractive interactions are performed. Upon cooling from random initial conditions, we find that the cones self assemble into clusters and that clusters…
Given a set $V$, a subset $S$, and a permutation $\pi$ of $V$, we say that $\pi$ permutes $S$ if $\pi (S) \cap S = \emptyset$. Given a collection $\cS = \{V; S_1,\ldots , S_m\}$, where $S_i \subseteq V ~~(i=1,\ldots ,m)$, we say that $\cS$…
We study the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let $ N>0 $ and $ L\in\mathbb{Z}_{\ge2} $. A multiple packing is a set…