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Concept

Discrete geometry

Related publications (29)

Cochains are all you need

Kelly Spry Maggs

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

Scalable constrained optimization

Maria-Luiza Vladarean

Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...

EPFL2024

Understanding the role of Hubbard corrections in the rhombohedral phase of BaTiO3

Nicola Marzari, Iurii Timrov, Michele Kotiuga, Lorenzo Bastonero

We present a first-principles study of the low-temperature rhombohedral phase of BaTiO3 using Hubbardcorrected density-functional theory. By employing density-functional perturbation theory, we compute the onsite Hubbard U for Ti(3d) states and the intersi ...

Amer Physical Soc2023

Spin dynamics, loop formation and cooperative reversal in artificial quasicrystals with tailored exchange coupling

Dirk Grundler, Sho Watanabe, Vinayak Shantaram Bhat

Aperiodicity and un-conventional rotational symmetries allow quasicrystalline structures to exhibit unusual physical and functional properties. In magnetism, artificial ferromagnetic quasicrystals exhibited knee anomalies suggesting reprogrammable magnetic ...

2023

Tomographic Volumetric Additive Manufacturing of Silicon Oxycarbide Ceramics

Jürgen Brugger, Christophe Moser, Damien Claude-Marie Loterie, Paul Delrot, Jorge Andres Madrid Wolff, Antoine Vincent Boniface, Georgia Konstantinou, Lorenz Hagelüken, Max Kollep

Ceramics are highly technical materials with properties of interest for multiple industries. Precisely because of their high chemical, thermal, and mechanical resistance, ceramics are difficult to mold into complex shapes. A possibility to make convoluted ...

2022

Discrete Voss surfaces: Designing geodesic gridshells with planar cladding panels

Corentin Jean Dominique Fivet, Nicolas Robin Montagne

The design and construction of doubly-curved structures often reveals to be challenging and can result in complex manufacturing and assembly. A recent strategy to tackle this difficulty consists in exploiting the connection between discrete differential ge ...

2022

Collapse-invariant properties of spaces equipped with signals or directions

Stefania Ebli

Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...

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

Generalised Implicit Neural Representations

Pierre Vandergheynst, Daniele Grattarola

We consider the problem of learning implicit neural representations (INRs) for signals on non-Euclidean domains. In the Euclidean case, INRs are trained on a discrete sampling of a signal over a regular lattice. Here, we assume that the continuous signal e ...

2022

Homogenization-based design of microstructured membranes: wake flows past permeable shells

François Gallaire, Edouard Boujo, Pier Giuseppe Ledda, Giuseppe Antonio Zampogna

A formal framework to characterize and control/optimize the flow past permeable membranes by means of a homogenization approach is proposed and applied to the wake flow past a permeable cylindrical shell. From a macroscopic viewpoint, a Navier-like effecti ...

Cambridge University Press2021

Voss surfaces: A design space for geodesic gridshells

Corentin Jean Dominique Fivet, Nicolas Robin Montagne

The design of envelopes with complex geometries often leads to construction challenges. To overcome these difficulties, resorting to discrete differential geometry proved successful by establishing close links between mesh properties and the existence of g ...

2021

Beyond Soft Hands: Efficient Grasping With Non-Anthropomorphic Soft Grippers

Yufei Hao

Grasping and manipulation are challenging tasks that are nonetheless critical for many robotic systems and applications. A century ago, robots were conceived as humanoid automata. While conceptual at the time, this viewpoint remains influential today. Many ...

FRONTIERS MEDIA SA2021

Adaptive Gradient Descent without Descent

We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the func ...

2020

Coordinate Difference Matrices

Martin Vetterli, Gilles Baechler, Golnooshsadat Elhami, Miranda Krekovic

In many problems such as phase retrieval, molecular biology, source localization, and sensor array calibration, one can measure vector differences between pairs of points and attempt to recover the position of these points; this class of problems is called ...

SIAM PUBLICATIONS2020

Optimum design of low environmental impact structures through component reuse

Jan Friedrich Georg Brütting

Load-bearing systems (structures) in buildings and infrastructure contribute to a significant share of adverse environmental impacts (EI) because of resource- and energy-intensive fabrication. A currently overlooked circular economy strategy to reduce EI i ...

EPFL2020

Investigation of the symmetry-breaking instability in a T-mixer with circular cross section

Lorenzo Siconolfi

This paper investigates the laminar flow inside a T-mixer composed of three pipes with a circular cross section. The flow enters the mixer symmetrically from the two aligned pipes and leaves the device from the third pipe. In similar devices, but involving ...

AMER INST PHYSICS2020

Voss Surfaces: A Design Space for Geodesic Gridshells

Corentin Jean Dominique Fivet, Nicolas Robin Montagne

2020

Mechanical Characterization of Integrally-Attached Timber Plate Structures: Experimental studies and macro modeling technique

Aryan Rezaei Rad

Spurred by the recent advancements in Computer-Aided Design (CAD), Integral Mechanical Attachment (IMA) technique has been resurrected. Using IMAs, connections between timber elements are established through their form, instead of using additional connecto ...

EPFL2020

Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval

Fabio Nobile, Yoshihito Kazashi

An existence result is presented for the dynamical low rank (DLR) approximation for random semi-linear evolutionary equations. The DLR solution approximates the true solution at each time instant by a linear combination of products of deterministic and sto ...

2021

Environmental impact minimization of reticular structures made of reused and new elements through Life Cycle Assessment and Mixed-Integer Linear Programming

Corentin Jean Dominique Fivet, Gennaro Senatore, Jan Friedrich Georg Brütting

An important share of building environmental impacts is embodied in load-bearing structures because of their large material mass and energy-intensive fabrication process. To reduce substantially material consumption and waste caused by the construction ind ...

2020