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We introduce a new type of $n$-dimensional generalization of symmetric $(v,k,\lambda)$ block designs. We prove upper bounds on the dimension $n$ in terms of $v$ and $k$. We also define the corresponding concept of $n$-dimensional difference…
Results of R. Stanley and M. Masuda completely characterize the h-vectors of simplicial posets whose order complexes are spheres. In this paper we examine the corresponding question in the case where the order complex is a ball. Using the…
In areas as diverse as contemporary art, play structures, climbing equipment, and modular construction toys, we see the presence of building block-like polyhedral complexes, which are generalizations of the pieces in the game Tetris. We…
Apart from a lot of fundamental interest, vector Bessel beams are widely used in optical manipulation, material processing, and imaging. However, the existing description of such beams remains fragmentary, especially when their scattering…
Nematic elastomers dramatically change their shape in response to diverse stimuli including light and heat. In this paper, we provide a systematic framework for the design of complex three dimensional shapes through the actuation of…
Shell mechanisms are patterned surface-like structures with compliant deformation modes that allow them to change shape drastically. Examples include many origami and kirigami tessellations as well as other periodic truss mechanisms. The…
Various microswimmers move along circles rather than straight lines due to their swimming mechanisms, body shapes or hydrodynamic effects. Here, we adopt the concepts of stochastic thermodynamics to analyze circle swimmers confined in a…
We consider the zero-energy deformations of periodic origami sheets with generic crease patterns. Using a mapping from the linear folding motions of such sheets to force-bearing modes in conjunction with the Maxwell-Calladine index theorem…
For centuries, human civilizations devised metal forming techniques to make tools and items; yet, customized metal forming remains costly and intricate. Laser-forming origami} (lasergami) is a metal forming process where a laser beam cuts…
It is well-known that many famous pooling designs are constructed from mathematical structures by the "containment matrix" method. In this paper, we propose another method and obtain a family of pooling designs with surprisingly high degree…
We survey results on the foldability of flat origami models. The main topics are the question of when a given crease pattern can fold flat, the combinatorics of mountain and valley creases, and counting how many ways a given crease pattern…
Among several models for microswimmers, the three-sphere microswimmer proposed by Najafi and Golestanian captures the essential mechanism for the locomotion of a microswimmer in a viscous fluid. Owing to its simplicity and flexibility, the…
Normalizing flows are a powerful tool for building expressive distributions in high dimensions. So far, most of the literature has concentrated on learning flows on Euclidean spaces. Some problems however, such as those involving angles,…
Tessellations of $R^3$ that use convex polyhedral cells to fill the space can be extremely complicated, especially if they are not facet-to-facet, that is, if the facets of a cell do not necessarily coincide with the facets of that cell's…
The topic of totally separable sphere packings is surveyed with a focus on regular constructions, uniform tilings, and contact number problems. An enumeration of all regular totally separable sphere packings in $\mathbb{R}^2$,…
The goal of this paper is to set up a framework designed to take into account the characteristics of sediment particles when transported by water. Our protocol consists in describing the characteristics of sediment particles via an…
The design of turbulence optimized stellarators has so far relied on three-dimensional equilibrium codes such as VMEC in order to find the minimum of a given objective function. In this work, we propose a complimentary approach based on the…
The interaction of a shock wave with a bubble features in many engineering and emerging technological applications, and has been used widely to test new numerical methods for compressible interfacial flows. Recently, density-based…
This paper deals with numerical methods for reconstruction of inhomogeneous conductivities. We use the concept of Generalized Polarization Tensors, which were introduced in [3], to do reconstruction. Basic resolution and stability analysis…
In this paper, we consider the problem of improving 2D triangle meshes tessellating planar regions. We propose a new variational principle for improving 2D triangle meshes where the energy functional is a convex function over the angle…