Concept

Geometric algebra

Related publications (165)

High-order geometric integrators for the variational Gaussian approximation

Among the single-trajectory Gaussian-based methods for solving the time-dependent Schrödinger equation, the variational Gaussian approximation is the most accurate one. In contrast to Heller’s original thawed Gaussian approximation, it is symplectic, conse ...

2023

Connecting Hodge and Sakaguchi-Kuramoto through a mathematical framework for coupled oscillators on simplicial complexes

Alexis Arnaudon

Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based on a recent formulation the Kuramoto model ...

NATURE PORTFOLIO2022

High-order geometric integrators for nonadiabatic molecular quantum dynamics and their applications to explore conical intersections

Seonghoon Choi

Accurate simulations of molecular quantum dynamics are crucial for understanding numerous natural processes and experimental results. Yet, such high-accuracy simulations are challenging even for relatively simple systems where the Born-Oppenheimer approxim ...

EPFL2022

Stabilized isogeometric discretizations on trimmed and union geometries, and weak imposition of the boundary conditions for the Darcy flow

Riccardo Puppi

Modern manufacturing engineering is based on a ``design-through-analysis'' workflow. According to this paradigm, a prototype is first designed with Computer-aided-design (CAD) software and then finalized by simulating its physical behavior, which usually i ...

EPFL2022

Spin Evolution in the Born-Oppenheimer Approximation

Jean-Philippe Ansermet, François Reuse, Klaus Maschke

The first part of this article attempts to highlight in chronological order some prominent papers that have direct connexion with the Born-Oppenheimer approximation. This timeline successively points to the role of level crossing, the notions of gauge fiel ...

WILEY-V C H VERLAG GMBH2022

MOCCA: Modeling and Optimizing Cone-joints for Complex Assemblies

Mark Pauly, Peng Song

We present a computational framework for modeling and optimizing complex assemblies using cone joints. Cone joints are integral joints that generalize traditional single-direction joints such as mortise and tenon joints to support a general cone of directi ...

ASSOC COMPUTING MACHINERY2021

Supersymmetries in nonequilibrium Langevin dynamics

Elisabeth Agoritsas

Stochastic phenomena are often described by Langevin equations, which serve as a mesoscopic model for microscopic dynamics. It has been known since the work of Parisi and Sourlas that reversible (or equilibrium) dynamics present supersymmetries (SUSYs). Th ...

2021

Immersed boundary-conformal isogeometric method for linear elliptic problems

Annalisa Buffa, Pablo Antolin Sanchez, Xiaodong Wei

We present a novel isogeometric method, namely the Immersed Boundary-Conformal Method (IBCM), that features a layer of discretization conformal to the boundary while employing a simple background mesh for the remaining domain. In this manner, we leverage t ...

2021

Fixed-wing micro UAV open data with digicam and raw INS/GNSS

Jan Skaloud, Davide Antonio Cucci, Kenneth Joseph Paul

We have recently released in the open domain data originating from a series of flights conducted with a fixed-wing micro UAV carrying high-quality small camera and navigation sensors. This data was previously used in several peer-reviewed publications. How ...

2021

Hyperbolic Fourier series

Maryna Viazovska

In this article we explain the essence of the interrelation described in [PNAS 118, 15 (2021)] on how to write explicit interpolation formula for solutions of the Klein-Gordon equation by using the recent Fourier pair interpolation formula of Viazovska and ...

arXiv2021

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