Publications associées à Forme différentielle

Cochains are all you need

In this thesis, we apply cochain complexes as an algebraic model of space in a diverse range of mathematical and scientific settings. We begin with an algebraic-discrete Morse theory model of auto-encoding cochain data, connecting the homotopy theory of d ...

EPFL2024

High order geometric methods with splines: fast solution with explicit time-stepping for Maxwell equations

Rafael Vazquez Hernandez, Bernard Kapidani

We introduce a high-order spline geometric approach for the initial boundary value problem for Maxwell's equations. The method is geometric in the sense that it discretizes in structure preserving fashion the two de Rham sequences of differential forms inv ...

2023

Eight-vertex criticality in the interacting Kitaev chain

Frédéric Mila, Natalia Chepiga

We show that including pairing and repulsion into the description of one-dimensional spinless fermions, as in the domain wall theory of commensurate melting or the interacting Kitaev chain, leads, for strong enough repulsion, to a line of critical points i ...

AMER PHYSICAL SOC2023

On the stress tensor light-ray operator algebra

Grégoire Olivier Mathys, Matthew Thomas Walters, Alexandre Mathieu Frédéric Belin

We study correlation functions involving generalized ANEC operators of the form integral dx-x-n+2T--x -> in four dimensions. We compute two, three, and ...

Springer Nature2021

On The Singular Set In The Thin Obstacle Problem: Higher-Order Blow-Ups And The Very Thin Obstacle Problem

Xavier Fernandez-Real Girona

We consider the singular set in the thin obstacle problem with weight vertical bar x(n +1)vertical bar(a) for a epsilon (-1, 1), which arises as the local extension of the obstacle problem for the fractional Laplacian (a nonlocal problem). We develop a ref ...

MATHEMATICAL SCIENCE PUBL2021

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

A Calculation Method for Interconnected Timber Elements Using Wood-Wood Connections

Yves Weinand, Julien Gamerro, Jean-François Bocquet

Wood-wood connections, widely used in the past, have been progressively replaced by steel fasteners in timber constructions. Currently, they can be manufactured and implemented more efficiently thanks to digital fabrication techniques. In addition, with th ...

2020

Synthetic Studies toward Amanita Phalloides Toxins

Philipp Georg Werner Seeberger

Amatoxins are ribosomally synthesized and post-translationally modified bicyclic octapeptides biosynthesized by the deadly basidiomycete fungus Amanita phalloides. Amongst this group, alpha-amanitin is the most widely known toxin and is currently under inv ...

EPFL2020

Einstein-Cartan gravity, matter, and scale-invariant generalization

Mikhail Chapochnikov, Andrey Shkerin, Inar Timiryasov, Sebastian Zell

We study gravity coupled to scalar and fermion fields in the Einstein-Cartan framework. We discuss the most general form of the action that contains terms of mass dimension not bigger than four, leaving out only contributions quadratic in curvature. By res ...

Springer Nature2020

Quasiconvexity and Relaxation in Optimal Transportation of Closed Differential Forms

Bernard Dacorogna

This manuscript extends the relaxation theory from nonlinear elasticity to electromagnetism and to actions defined on paths of differential forms. The introduction of a gauge allows for a reformulation of the notion of quasiconvexity in Bandyopadhyay et al ...

SPRINGER2019