Concept

Gauss–Bonnet theorem

Related publications (27)

Electronic transport in graphene with out-of-plane disorder

Real-world samples of graphene often exhibit various types of out-of-plane disorder-ripples, wrinkles and folds-introduced at the stage of growth and transfer processes. These complex out-of-plane defects resulting from the interplay between self-adhesion ...

Berlin2024

Comparing the Buckling Strength of Spherical Shells With Dimpled Versus Bumpy Defects

Pedro Miguel Nunes Pereira de Almeida Reis, Fani Derveni, Arefeh Abbasi

We investigate the effect of defect geometry in dictating the sensitivity of the critical buckling conditions of spherical shells under external pressure loading. Specifically, we perform a comparative study between shells containing dimpled (inward) versu ...

ASME2023

Piecewise Affine Curvature model: a reduced-order model for soft robot-environment interaction beyond PCC

Josephine Anna Eleanor Hughes, Francesco Stella, Qinghua Guan

Soft robot are celebrated for their propensity to enable compliant and complex robot-environment interactions. Soft robotic manipulators, or slender continuum structure robots have the potential to exploit these interactions to enable new exploration and m ...

IEEE2023

Compact, spatial-mode-interaction-free, ultralow-loss, nonlinear photonic integrated circuits

Tobias Kippenberg, Rui Ning Wang, Xinru Ji, Zheru Qiu, Junqiu Liu, Jijun He

Multi-mode waveguides are ubiquitously used in integrated photonics. Although interaction among different spatial waveguide eigenmodes can induce novel nonlinear phenomena, spatial mode interaction is typically undesired. Adiabatic bends, such as Euler ben ...

NATURE PORTFOLIO2022

Amphiphilic nanoparticles generate curvature in lipid membranes and shape liposome-liposome interfaces

Francesco Stellacci, Francesca Olgiati

We show by molecular dynamics that amphiphilic Au nanoparticles (NP) with a diameter of 4 nm generate curvature in phosphatidylcholine lipid membranes. NPs generate negative curvature when they adsorb on the membrane surface but, as they get spontaneously ...

ROYAL SOC CHEMISTRY2021

How to weave a perfect sphere with curved strips

Mark Pauly, Tian Chen, Yingying Ren

Triaxial weaving, a craft technique that enables the generation of surfaces with tri-directional arrays of initially straight elastic strips, has long been loved by basket makers and artists seeking a combination of practical and aesthetically-pleasing str ...

American Physical Society2020

A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

Adrien Giuliano Marcone

The purpose of this thesis is to provide an intrinsic proof of a Gauss-Bonnet-Chern formula for complete Riemannian manifolds with finitely many conical singularities and asymptotically conical ends. A geometric invariant is associated to the link of both ...

EPFL2019

Smooth Shapes with Spherical Topology: Beyond Traditional Modeling, Efficient Deformation, and Interaction

Michaël Unser, Pablo Garcia-Amorena Garcia, Daniel Andreas Schmitter

Existing shape models with spherical topology are typically designed either in the discrete domain using interpolating polygon meshes or in the continuous domain using smooth but non-interpolating schemes such as subdivision or NURBS. Both polygon models a ...

2017

Generalized Gauss Inequalities via Semidefinite Programming

Daniel Kuhn

A sharp upper bound on the probability of a random vector falling outside a polytope, based solely on the first and second moments of its distribution, can be computed efficiently using semidefinite programming. However, this Chebyshev-type bound tends to ...

Springer Verlag2016

Smoothly Deformable Spheres: Modeling, Deformation, and Interaction

Michaël Unser, Pablo Garcia-Amorena Garcia, Daniel Andreas Schmitter

ACM2016

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