Publications related to Poincaré half-plane model

Well-posedness Issues For the Half-Wave Maps Equation With Hyperbolic And Spherical Targets

This thesis is a study of the global well-posedness of the Cauchy problems for half-wave maps from the Minkowski space of dimension n+1 to the 2-dimensional sphere and the hyperbolic plane. The work is mainly based on the results from Krieger-Sire 17' in ...

EPFL2023

A full characterization of invariant embeddability of unimodular planar graphs

Laszlo Marton Toth

When can a unimodular random planar graph be drawn in the Euclidean or the hyperbolic plane in a way that the distribution of the random drawing is isometry-invariant? This question was answered for one-ended unimodular graphs in Benjamini and Timar, using ...

WILEY2023

Determining crack kinematics from imaged crack patterns

Katrin Beyer, Bryan German Pantoja Rosero, Amir Rezaie, Ketson Roberto Maximiano Dos Santos

Determining the relationship between the cause of damage and the subsequent structural behavior of infrastructure systems requires an accurate characterization of the propagation of cracks, which represents the evolution of the damage state. When no inform ...

2022

Shapes From Echoes: Uniqueness From Point-to-Plane Distance Matrices

Martin Vetterli, Ivan Dokmanic, Miranda Krekovic

We study the problem of localizing a configuration of points and planes from the collection of point-to-plane distances. This problem models simultaneous localization and mapping from acoustic echoes as well as the & x201C;structure from sound & x201D; app ...

2020

Characterization of the traces on the boundary of functions in magnetic Sobolev spaces

Hoài-Minh Nguyên

We characterize the trace of magnetic Sobolev spaces defined in a half-space or in a smooth bounded domain in which the magnetic field Ais differentiable and its exterior derivative corresponding to the magnetic field dAis bounded. In particular, we prove ...

2020

Scattering of SH-waves by an elliptic cavity/crack beneath the interface between functionally graded and homogeneous half-spaces via multipole expansion method

Alireza Ghafarollahi

In this study, based on multipole expansion method an analytical treatment is presented for the anti-plane scattering of SH-waves by an arbitrarily oriented elliptic cavity/crack which is embedded near the interface between exponentially graded and homogen ...

2018

Minimal entropy for uniform lattices in product of hyperbolic planes

Louis Georges Eric Merlin

Let M be a quotient of H-2 x ... x H-2 (product of hyperbolic planes) by a uniform lattice of. PSL2(R))(n). We prove that, among metrics of M of prescribed volume, the sum of hyperbolic metrics has minimal volume entropy. ...

European Mathematical Soc2016

SHAPE: Linear-Time Camera Pose Estimation With Quadratic Error-Decay

Martin Vetterli, Adam James Scholefield, Alireza Ghasemi

We propose a novel camera pose estimation or perspective-n-point (PnP) algorithm, based on the idea of consistency regions and half-space intersections. Our algorithm has linear time-complexity and a squared reconstruction error that decreases at least qua ...

Ieee2016

General coordinate invariance in quantum many-body systems

Alexander Monin, Solomon G Shamsuddin Osman Endlich

We extend the notion of general coordinate invariance to many-body, not necessarily relativistic, systems. As an application, we investigate nonrelativistic general covariance in Galilei-invariant systems. The peculiar transformation rules for the backgrou ...

American Physical Society2014

(Re-)inventing the relativistic wheel: gravity, cosets, and spinning objects

Francesco Riva, Alexander Monin, Solomon G Shamsuddin Osman Endlich

Space-time symmetries are a crucial ingredient of any theoretical model in physics. Unlike internal symmetries, which may or may not be gauged and/or spontaneously broken, space-time symmetries do not admit any ambiguity: they are gauged by gravity, and an ...

Springer Nature2014

An Exotic Deformation of the Hyperbolic Space

Nicolas Monod

Let Isom(H^n) be the group of isometries of the n-dimensional real hyperbolic space. We first classify all continuous non-elementary actions of on the infinite-dimensional real hyperbolic space. We then prove the existence of a continuous family of non-iso ...

Johns Hopkins Univ Press2014

On some convex cocompact groups in real hyperbolic space

Marc Desgroseilliers

We generalize to a wider class of hyperbolic groups a construction by Misha Kapovich yielding convex cocompact representations into real hyperbolic space. ...

Geometry & Topology Publications2013

Closing Large Hyperbolic 2g-gons : a Way to Study Hyperelliptic Riemann Surfaces of Genus g

Poincaré's uniformisation theorem says that any Riemann surface is conformally equivalent to a unique (up to isometry) surface of constant Gauss curvature 0, 1 or –1. The (topologically) richest of these three worlds is for curvature –1 formed of hyperboli ...

EPFL2012

Third-harmonic generation microscopy with Bessel beams: a numerical study

We study theoretically and numerically third-harmonic generation (THG) from model geometries (interfaces, slabs, periodic media) illuminated by Bessel beams produced by focusing an annular intensity profile. Bessel beams exhibit a phase and intensity distr ...

Optical Soc Amer2012

Invariant Higher-Order Variational Problems II

Tudor Ratiu, François Gay-Balmaz

Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as ...

Springer Verlag2012

Finite Element Method on Riemann Surfaces and Applications to the Laplacian Spectrum

Marc Maintrot

The objective of this PhD thesis is the approximate computation of the solutions of the Spectral Problem associated with the Laplace operator on a compact Riemann surface without boundaries. A Riemann surface can be seen as a gluing of portions of the Hype ...

EPFL2012

Three-dimensional granular model of semi-solid metallic alloys undergoing solidification: Fluid flow and localization of feeding

Michel Rappaz, Jean-Marie Drezet, André Phillion, Meisam Sistaninia

A three-dimensional (3-D) granular model which simulates fluid flow within solidifying alloys with a globular microstructure, such as that found in grain refined Al alloys, is presented. The model geometry within a representative volume element (RVE) consi ...

Elsevier2012

Stabilization of the cart-pendulum system through approximate manifold decomposition

Dominique Bonvin, Philippe Müllhaupt, David Ingram

This paper proposes a feedback law capable of swinging up and stabilizing the cartpendulum system. The approach uses an iterative algorithm that is typically used to construct a locally linearizing output for nonlinear control-affine systems. However, rath ...

2011

Rotationally resolved studies of S-0 and the exciton coupled S-1/S-2 origin regions of diphenylmethane and the d(12) isotopologue

Rotationally resolved microwave and ultraviolet spectra of jet-cooled diphenylmethane (DPM) and DPM-d(12) have been obtained in S-0, S-1, and S-2 electronic states using Fourier-transform microwave and UV laser/molecular beam spectrometers. The S-0 and S-1 ...

2008