Related papers: On the Shape Containment Problem within the Amoebo…
The Arbitrary Pattern Formation problem asks for a distributed algorithm that moves a set of autonomous mobile robots to form any arbitrary pattern given as input. The robots are assumed to be autonomous, anonymous and identical. They…
Shape completion is the problem of completing partial input shapes such as partial scans. This problem finds important applications in computer vision and robotics due to issues such as occlusion or sparsity in real-world data. However,…
Designing reconfigurable materials based on deformable nanoparticles (NPs) hinges on an understanding of the energetically-favored shapes these NPs can adopt. Using simulations, we show that hollow, deformable patchy NPs tailored with…
The central object of this PhD thesis is known under different names in the fields of computer science and statistical mechanics. In computer science, it is called the Maximum Cut problem, one of the famous twenty-one Karp's original…
Our work is motivated by the challenges presented in preparing arrays of atoms for use in quantum simulation. The recently-developed process of loading atoms into traps results in approximately half of the traps being filled. To consolidate…
Amorphous materials of homogeneous structures usually suffer from nonuniform deformation under shear, which can develop into shear localization and eventually destructive shear band. One approach to tackle this issue is to introduce an…
Run-and-tumble particles constitute one of the simplest models of self-propelled active matter, and provide an ideal playground to the understanding of out-of-equilibrium systems. We consider an idealized setup where one such particle is…
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…
We revisit a standard polygon containment problem: given a convex $k$-gon $P$ and a convex $n$-gon $Q$ in the plane, find a placement of $P$ inside $Q$ under translation and rotation (if it exists), or more generally, find the largest copy…
Systems of identical particles with equal charge are studied under a special type of confinement. These classical particles are free to move inside some convex region S and on the boundary of it $\Omega$ (the $S^{d-1}-$ sphere, in our…
This paper presents a computational approach for finding the optimal shapes of peristaltic pumps transporting rigid particles in Stokes flow. In particular, we consider shapes that minimize the rate of energy dissipation while pumping a…
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…
Optimization problems associated with the interaction of linked particles are at the heart of polymer science, protein folding and other important problems in the physical sciences. In this review we explain how to recast these problems as…
Structured optimization problems are ubiquitous in fields like data science and engineering. The goal in structured optimization is using a prescribed set of points, called atoms, to build up a solution that minimizes or maximizes a given…
This article is devoted to the shape optimization of the internal structure of an electric motor, and more precisely of the arrangement of air and ferromagnetic material inside the rotor part with the aim to increase the torque of the…
Real-life man-made objects often exhibit strong and easily-identifiable structure, as a direct result of their design or their intended functionality. Structure typically appears in the form of individual parts and their arrangement.…
We propose a PDE-constrained shape registration algorithm that captures the deformation and growth of biological tissue from imaging data. Shape registration is the process of evaluating optimum alignment between pairs of geometries through…
Recent advancements in the synthesis of anisotropic macromolecules and nanoparticles have spurred an immense interest in theoretical and computational studies of self-assembly. The cornerstone of such studies is the role of shape in…
We simulate a two dimensional model of self-propelled particles confined by a deformable boundary. The particles tend to accumulate near the boundary and the shape of the boundary deforms upon the collisions. We find that there are two…
Programmable arrays of optical traps enable the assembly of configurations of single atoms to perform controlled experiments on quantum many-body systems. Finding the sequence of control operations to transform an arbitrary configuration of…