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In the framework of algebraic topology the closed sequence of 4-dimensional polyhedra (algebraic polytopes) was defined. This sequence is started by the polytope {240}, discovered by Coxeter, and is determined by the second coordination…
In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The…
This paper deals with shape irregularity issues in discrete topology optimization algorithms whereby the design is created using the automated distribution of material in the design region. Graph theory is employed to derive appropriate…
Building structures with hierarchical order through the self-assembly of smaller blocks is not only a prerogative of nature, but also a strategy to design artificial materials with tailored functions. We explore in simulation the…
The nucleation kinetics of the rotator phase in hard cuboctahedra, truncated octahedra, and rhombic dodecahedra is simulated via a combination of Forward Flux Sampling and Umbrella Sampling. For comparable degree of supersaturation, the…
We investigate by scattering techniques the structure of water-based soft composite materials comprising a crystal made of Pluronic block-copolymer micelles arranged in a face-centered cubic lattice and a small amount (at most 2% by volume)…
Packing problems have been of great interest in many diverse contexts for many centuries. The optimal packing of identical objects has been often invoked to understand the nature of low temperature phases of matter. In celebrated work,…
Molecular building blocks interacting at the nanoscale organize spontaneously into stable mono- layers that display intriguing long-range ordering motifs on the surface of atomic substrates. The patterning process, if appropriately…
The ability to pattern the location of pillars in epitaxial matrix-pillar nanocomposites is a key challenge to develop future technologies using these intriguing materials. One such model system employs a ferrimagnetic CoFe$_{2}$O$_{4}$…
Over the past two decades polymer nanocomposites have received tremendous interest from industry and academia due to their advanced properties comparative to polymer blends. Many computational studies have revealed that the macroscopic…
We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into…
This work deals with the presence of topological structures in models of two real scalar fields in the two-dimensional spacetime. The subject concerns the presence of a geometric constriction, which appears with a modification of the…
A simple optical strategy to transform patchy PMMA azopolymer composite nanoparticles into complex, fully three-dimensional morphologies using controlled laser polarization is presented. The particles consist of a PMMA core decorated with…
Combinatorial algorithms are widely used for decision-making and knowledge discovery, and it is important to ensure that their output remains stable even when subjected to small perturbations in the input. Failure to do so can lead to…
In the frameworks of algebraic topology {\alpha}-helix and different DNA-conformations are determined as the local latticed packing, confined by peculiar minimal surfaces which are similar to helicoids. These structures are defined by…
We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that…
In spectral clustering, one defines a similarity matrix for a collection of data points, transforms the matrix to get the Laplacian matrix, finds the eigenvectors of the Laplacian matrix, and obtains a partition of the data using the…
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…
We use soft x-ray vector-ptychographic tomography to determine the three-dimensional magnetization field in superparamagnetic nanoparticles self-assembled at the liquid-liquid interface and reveal the magnetic order induced by layered…
The problem of diagonalizing a class of complicated matrices, to be called ultrametric matrices, is investigated. These matrices appear at various stages in the description of disordered systems with many equilibrium phases by the technique…