Research
Research
Research
Research
316+ open-access research outputs.
If a finite group $G$ acts on a rational homology manifold, then the orbit space is well-known to be a rational homology manifold again. We consider here actions on spaces that may be much more singul…
Beam theory has traditionally been restricted to small elastic strains and rigid cross-sections. Relaxing these assumptions within closed-form analytical frameworks remains challenging. In contrast, t…
This paper presents a pressure-robust and element-wise divergence-free nonconforming finite element method for the Stokes problem on curved domains. The discrete element is constructed by mapping the …
When three-dimensional bodies contain thin features, non-trivial topology, or scan-derived surfaces, volumetric meshing can become the dominant bottleneck in simulation workflows. We replace this step…
In this paper, we propose two monolithic fully discrete finite element methods for fluid-structure interaction (FSI) based on a novel Piola-type Arbitrary Lagrangian-Eulerian (ALE) mapping. For the te…
We present a stable finite element method for incompressible nonlinear elasticity based on a four-field mixed formulation involving the displacement, displacement gradient, first Piola--Kirchhoff stre…
Combinatorial optimization problems are central to science and engineering and specialized hardware from quantum annealers to classical Ising machines are being actively developed to address them. The…
Grid diagrams are special representations of knots in the three-sphere that are used to define a combinatorial version of knot Floer homology. Paolo Ghiggini and Yi Ni showed that knot Floer homology …
This study proposes and analyses a novel higher-order, structure preserving discretization method for inviscid barotropic flows from a Lagrangian perspective. The method is built on a multisymplectic …
The DataSquad at Carleton College addresses a common problem at small liberal arts colleges: limited capacity for data services and few opportunities for students to gain practical experience with dat…
We investigate the Lieb--Liniger model of interacting one-dimensional bosons coupled to a localized impurity, modeled by a delta barrier. While the Lieb--Liniger gas is integrable, the impurity breaks…
In this paper we discuss a one-dimensional model for two-phase Enhanced Oil Recovery (EOR) floods, primarily for the polymer flood. We improve upon the method for the construction of semi-analytical s…
Thermalization of a closed chaotic quantum system is commonly addressed in terms of the eigenstate thermalization hypothesis (ETH). An alternative approach uses the Bohigas-Giannoni-Schmit (BGS) conje…
We present a methodology to model articulated objects using a sparse set of images with unknown poses. Current methods require dense multi-view observations and ground-truth camera poses. Our approa…
There are multiple generalisations of the Pythagorean theorem to spherical and hyperbolic geometry. A natural one, involving areas of disks with radii equal to the sides of a proper triangle, was disc…
We derive a discrete $ L^q-L^p$ Sobolev inequality tailored for the Crouzeix--Raviart and discontinuous Crouzeix--Raviart finite element spaces on anisotropic meshes in both two and three dimensions. …
Non-manual signals in sign languages continue to be a challenge for signing avatars. More specifically, emotional content has been difficult to incorporate because of a lack of a standard method of sp…
Coarse room layout estimation provides important geometric cues for many downstream tasks. Current state-of-the-art methods are predominantly based on single views and often assume panoramic images. W…
We introduce a generalized \textit{Probabilistic Approximate Optimization Algorithm (PAOA)}, a classical variational Monte Carlo framework that extends and formalizes prior work by Weitz \textit{et al…
Climate tipping points are critical thresholds in Earth's climate system where a small change can cause abrupt and potentially irreversible shifts towards a new state. Tipping points in the Atlantic M…
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