Platonic solid

Formal sciences
Mathematics
Geometry
Euclidean geometry

Related publications (26)

Finite Element Modeling of Tight Elastic Knots

Pedro Miguel Nunes Pereira de Almeida Reis, Tomohiko Sano, Paul Johanns, Changyeob Baek, Paul Grandgeorge

We present a methodology to simulate the mechanics of knots in elastic rods using geometrically nonlinear, full three-dimensional (3D) finite element analysis. We focus on the mechanical behavior of knots in tight configurations, for which the full 3D defo ...

2020

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Homonuclear Decoupling in H-1 NMR of Solids by Remote Correlation

David Lyndon Emsley, Gabriele Stevanato, Pinelopi Moutzouri, Federico Maria Paruzzo, Bruno Simões de Almeida

The typical linewidths of H-1 NMR spectra of powdered organic solids at 111 kHz magic-angle spinning (MAS) are of the order of a few hundred Hz. While this is remarkable in comparison to the tens of kHz observed in spectra of static samples, it is still th ...

Wiley-VCH Verlag GmbH2020

Finite Element Modeling of Tight Elastic Knots

Pedro Miguel Nunes Pereira de Almeida Reis, Tomohiko Sano, Paul Johanns, Changyeob Baek, Paul Grandgeorge

2020

Melting of a skyrmion lattice to a skyrmion liquid via a hexatic phase

Henrik Moodysson Rønnow, Arnaud Magrez, Marco Cantoni, Fabrizio Carbone, Ping Huang, Thomas Schönenberger

While in 3D materials melting is a single, first-order phase transition, in 2D systems, it can also proceed via an intermediate phase. For a skyrmion lattice in Cu2OSeO3, magnetic field variations can tune this quasiparticle 2D solid into a skyrmion liquid ...

Nature Publishing Group2020

Functional Inverse Problems on Spheres: Theory, Algorithms and Applications

Matthieu Martin Jean-André Simeoni

Many scientific inquiries in natural sciences involve approximating a spherical field -namely a scalar quantity defined over a continuum of directions- from generalised samples of the latter (e.g. directional samples, local averages, etc). Such an approxim ...

EPFL2020

Fast and ultrafast electron microscopies for skyrmions and plasmonics

Gabriele Berruto

In recent years, topology gained a central role in physics. We learnt that energetics could be often explained better by classes of objects defined by having qualitative differences. In today's jargon, we say they are topologically distinct. The process of ...

EPFL2019

Semiconductor Nanowires: To Grow or Not to Grow?

Anna Fontcuberta i Morral

Semiconductor nanowires have demonstrated exciting properties for nanophotonics, sensors, energy technologies and end-of-roadmap and beyond-roadmap electronic devices. Fabrication schemes for nanowires are varied, but they fall into three general categorie ...

2019

Nested Convex Bodies are Chaseable

Marek Elias

In the Convex Body Chasing problem, we are given an initial point v0. Rd and an online sequence of n convex bodies F1,..., Fn. When we receive Ft, we are required to move inside Ft. Our goal is to minimize the total distance traveled. This fundamental onli ...

SPRINGER2020

On the reverse isodiametric problem and Dvoretzky-Rogers-type volume bounds

Matthias Schymura

The isodiametric inequality states that the Euclidean ball maximizes the volume among all convex bodies of a given diameter. We are motivated by a conjecture of Makai Jr. on the reverse question: Every convex body has a linear image whose isodiametric quot ...

2018

Temperature Dependence of the Vacancy Formation Energy in Solid He-4

Riccardo Rota

We studied the thermal effects on the behavior of incommensurate solid He-4 at low temperatures using the path integral Monte Carlo method. Below a certain temperature, depending on the density and the structure of the crystal, the vacancies delocalize and ...

2018

Full Phase Diagram of Active Brownian Disks: From Melting to Motility-Induced Phase Separation

Ignacio Pagonabarraga Mora, Pasquale Digregorio

We establish the complete phase diagram of self-propelled hard disks in two spatial dimensions from the analysis of the equation of state and the statistics of local order parameters. The equilibrium melting scenario is maintained at small activities, with ...

2018

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