相关论文: Element sets for high-order Poincar\'e mapping of …

I formulate a general finite element method (FEM) for self-gravitating stellar systems. I split the configuration space to finite elements, and express the potential and density functions over each element in terms of their nodal values and…

An algorithm for detecting periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp.~6172--6175], which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp.~4733--4736]…

This study explores reduced-order modeling for analyzing the time-dependent diffusion-deformation of hydrogels. The full-order model describing hydrogel transient behavior consists of a coupled system of partial differential equations in…

In recent years, stable and unstable manifolds of invariant objects (such as libration points and periodic orbits) have been increasingly recognized as an efficient tool for designing transfer trajectories in space missions. However, most…

Perturbative approaches are methods to efficiently tackle many-body problems, offering both intuitive insights and analysis of correlation effects. However, their application to systems where light and matter are strongly coupled is…

This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…

We construct finite element de~Rham complexes of higher and possibly non-uniform polynomial order in finite element exterior calculus (FEEC). Starting from the finite element differential complex of lowest-order, known as the complex of…

Optimal transport provides a powerful framework for comparing measures while respecting the geometry of their support, but comes with an expensive computational cost, hindering its potential application to real world use cases. On…

Optimal Transport (OT) theory investigates the cost-minimizing transport map that moves a source distribution to a target distribution. Recently, several approaches have emerged for learning the optimal transport map for a given cost…

The Kepler mission was launched in 2009 and has discovered thousands of planet candidates. In a recent paper, Esteves et al. (2013) found a periodic signal in the light curves of KOI-13 and HAT-P-7, with a frequency triple the orbital…

The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…

We propose a high order numerical homogenization method for dissipative ordinary differential equations (ODEs) containing two time scales. Essentially, only first order homogenized model globally in time can be derived. To achieve a high…

In this work, we develop and analyze a higher-order finite element method for the multidimensional fragmentation equation. To the best of our knowledge, this is the first study to establish a rigorous, conforming finite element framework…

Hamiltonian operator inference has been developed in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method…

The merits of a perturbation theory based on a mean to osculating transformation that is pure periodic in the fast angle are investigated. The exact separation of the purely short-period effects of the perturbed Keplerian dynamics from the…

Mapping exoplanets across phases and during secondary eclipse is a powerful technique for characterizing Hot Jupiters in emission. Since these planets are expected to rotate about axes normal to their orbital planes, with rotation periods…

A crucial step in planet hunting surveys is to select the best candidates for follow up observations, given limited telescope resources. This is often performed by human `eyeballing', a time consuming and statistically awkward process. Here…

Multi-principal element materials (MPEMs) have been attracting a rapidly growing interest due to their exceptional performance under extreme conditions, from cryogenic conditions to extreme-high temperatures and pressures. Despite the…

We study exceptional points (EPs) of a nonhermitian Hamiltonian $\hat{H}(\lambda,\delta)$ whose parameters $\lambda \in {\mathbb C}$ and $\delta \in {\mathbb R}$. As the real control parameter $\delta$ is varied, the $k$-th EP (or $k$-th…

Ordered phases of matter, such as solids, ferromagnets, superfluids, or quantum topological order, typically only exist at low temperatures. Despite this conventional wisdom, we present explicit local models in which all such phases persist…