Related papers: Identifying Phase Space Boundaries with Voronoi Te…
A body $\Theta$ containing two phases, which may form a periodic composite with microstructure much smaller that the body, or which may have structure on a length scale comparable to the body, is subjected to slowly time varying boundary…
We propose a new strategy to systematically search for new physics processes in particle collisions at the energy frontier. An examination of all possible topologies which give identifiable resonant features in a specific final state leads…
We introduce a differentiable 3D representation that unifies the ray tracing capabilities of foam-based ray tracing with the efficiency of modern rasterization pipelines. While prior foam representations enable constant-time ray traversal…
Power diagrams, a type of weighted Voronoi diagrams, have many applications throughout operations research. We study the problem of power diagram detection: determining whether a given finite partition of $\mathbb{R}^d$ takes the form of a…
We present a method for computing the 6-dimensional coarse-grained phase-space density $f(x,v)$ in an N-body system, and derive its distribution function $v(f)$. The method is based on Delaunay tessellation, where $v(f)$ is obtained with an…
Disordered hyperuniform packings are unusual amorphous states of two-phase materials that are endowed with exotic physical properties. Such hyperuniform systems are characterized by an anomalous suppression of volume-fraction fluctuations…
Networks generated from Voronoi tessellations of space are prototypes for topologically disordered systems. In order to assess the effects of random coordination on the statistical properties of energy spectra, we analyze tight-binding…
Broad classes of plasma phenomena can be understood in terms of phase-space rearrangements. For example, the net effect of a wave-particle interaction may consist of moving populations of particles from one region of phase space to another.…
A Voronoi diagram partitions the plane into convex cells, each containing the points closest to a single generator. Given such a tessellation, the inverse Voronoi problem seeks the generator set \( S \) that produced it. Our algorithm…
Testing of the disjunction hypothesis is appropriate when each gene or location studied is associated with multiple $p$-values, each of which is of individual interest. This can occur when more than one aspect of an underlying process is…
Cell deformability is an essential determinant for tissue-scale mechanical nature, such as fluidity and rigidity, and is thus crucial for understanding tissue homeostasis and stable developmental processes. However, numerical simulations…
Biomolecular condensates form on timescales of seconds in cells upon environmental or compositional changes. Condensate formation is thus argued to act as a mechanism for sensing such changes and quickly initiating downstream processes,…
The detection of phase transitions is a fundamental challenge in condensed matter physics, traditionally addressed through analytical methods and direct numerical simulations. In recent years, machine learning techniques have emerged as…
We address the problem of analytically extracting a countable infinity of flat, non-dispersive bands in a periodic array of cells that comprise branching Vicsek geometries of higher and higher generations. Through a geometric construction,…
Gersho's conjecture in 3D asserts the asymptotic periodicity and structure of the optimal centroidal Voronoi tessellation. This relatively simple crystallization problem remains to date open. We prove bounds on the geometric complexity of…
Cosmic voids, the large underdense regions of our Universe, have emerged over the past decade as powerful cosmological laboratories: their simple dynamics, sensitivity to local gravitational effects and cosmic expansion, and ability to span…
Recent discoveries have demonstrated that matter can be distinguished on the basis of topological considerations, giving rise to the concept of topological phase. Introduced originally in condensed matter physics, the physics of topological…
We introduce a new method to identify phase boundaries in physical systems. It is based on training a predictive model such as a neural network to infer a physical system's parameters from its state. The deviation of the inferred parameters…
The definition of the phase space of field theories in presence of boundaries of Cauchy surfaces requires a choice of boundary conditions or decay behaviour of those fields. Often these conditions are motivated in part by the decay…
Calculations on atomistic scale are necessary for understanding of physical phenomena occurring during advanced processing of liquids, slurries, and nano-ceramics composite materials. This paper describes some new ideas for using the…