Publications related to Harmonic map

High-order geometric integrators for the variational Gaussian wavepacket dynamics and application to vibronic spectra at finite temperature

Molecular quantum dynamics simulations are essential for understanding many fundamental phenomena in physics and chemistry. They often require solving the time-dependent Schrödinger equation for molecular nuclei, which is challenging even for medium-sized ...

EPFL2024

Semi-global controllability of a geometric wave equation

Joachim Krieger, Shengquan Xiang

We prove the semi-global controllability and stabilization of the

(1+1)-

dimensional wave maps equation with spatial domain 𝕊1 and target

𝕊k

. First we show that damping stabilizes the system when the energy is strictly below the threshold

2π

, where ha ...

2022

Self-Structuring Of Cellular And Channel Type In Complex System Dynamics In The Framework Of Scale Relativity Theory

Maria-Alexandra Paun

In the framework of Scale Relativity Theory, by analyzing dynamics of complex system structural units based on multifractal curves, both Schrodinger and Madelung approaches are functional and complementary. The Madelung selected approach involve synchronou ...

UNIV POLITEHNICA BUCHAREST, SCI BULL2022

Ab initio semiclassical evaluation of vibrationally resolved electronic spectra with thawed Gaussians

Jiri Vanicek, Tomislav Begusic

Vibrationally resolved electronic spectra of polyatomic molecules provide valuable information about the quantum properties of both electrons and nuclei. This chapter reviews the recent progress in ab initio semiclassical calculations of such spectra, base ...

Elsevier2021

A stability theory beyond the co-rotational setting for critical wave maps blow up

Joachim Krieger, Shuang Miao

We exhibit non-equivariant perturbations of the blowup solutions constructed in [18] for energy critical wave maps into

\mathbb{S}^2

. Our admissible class of perturbations is an open set in some sufficiently smooth topology and vanishes near the light co ...

2020

Some regularity results for p-harmonic mappings between Riemannian manifolds

Changyu Guo

Let M be a C-2-smooth Riemannian manifold with boundary and N a complete C-2-smooth Riemannian manifold. We show that each stationary p-harmonic mapping u: M -> N, whose image lies in a compact subset of N, is locally C-1,C-alpha for some alpha is an eleme ...

2019

The index of singular zeros of harmonic mappings of anti-analytic degree one

Robert Gerhard Jérôme Luce

We study harmonic mappings of the form , where h is an analytic function. In particular, we are interested in the index (a generalized multiplicity) of the zeros of such functions. Outside the critical set of f, where the Jacobian of f is non-vanishing, it ...

TAYLOR & FRANCIS LTD2021

Second Harmonic Generation Dynamics in Plasmonic Nanoparticles

Olivier Martin, Jérémy Butet, Gabriel David Bernasconi

Due to its symmetry properties, second-harmonic generation in plasmonic nanostructures enables the observation of even-parity modes that couple weakly to the far field. Consequentially, those modes radiate less and thus have a longer lifetime. Using a full ...

SPIE-INT SOC OPTICAL ENGINEERING2018

On-the-Fly Ab Initio Semiclassical Evaluation of Absorption Spectra of Polyatomic Molecules beyond the Condon Approximation

Jiri Vanicek, Aurélien Kevin Fabrice Patoz, Tomislav Begusic

To evaluate vibronic spectra beyond the Condon approximation, we extend the on-the-fly ab initio thawed Gaussian approximation by considering the Herzberg–Teller contribution due to the dependence of the electronic transition dipole moment on nuclear coord ...

2018

Renormalization and blow up for wave maps from $S^2 \times \mathbb{R}$ to $S^2$

Sohrab Mirshams Shahshahani

We construct a one parameter family of nite time blow ups to the co-rotational wave maps problem from

S^2\times R

to

S^2

parameterized by

\nu \epsilon (\frac{1}{2},1]

. The longitudinal function

u(t,\alpha)

which is the main object of study will be ...

2016

Optimal polynomial blow up range for critical wave maps

Joachim Krieger, Can Gao

We prove that the critical Wave Maps equation with target

S^2

and origin

\R^{2+1}

admits energy class blow up solutions of the form

u(t, r) = Q(\lambda(t)r) + \eps(t, r)

where

Q:\R^2\rightarrow S^2

is the ground state harmonic map and $\lambd ...

2015

Harmonic Singular Integrals and Steerable Wavelets in $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

Michaël Unser, John Paul Ward

Here we present a method of constructing steerable wavelet frames in

L _{ 2 }

(\mathbb{R} ^{ d }

) that generalizes and unifies previous approaches, including Simoncelli's pyramid and Riesz wavelets. The motivation for steerable wavelets is the nee ...

Elsevier2014

Harmonic Maps on Smooth Metric Measure Spaces and on Riemannian Polyhedra

Zahra Sinaei

This thesis is a study of harmonic maps in two different settings. The first part is concerned with harmonic maps from smooth metric measure spaces to Riemannian manifolds. The second part is study of harmonic maps from Riemannian polyhedra to non-positive ...

EPFL2013

Laplacian Meshes for Monocular 3D Shape Recovery

Pascal Fua, Aydin Varol, Tien Dat Ngo, Jonas Olof Martin Östlund

We show that by extending the Laplacian formalism, which was first introduced in the Graphics community to regularize 3D meshes, we can turn the monocular 3D shape reconstruction of a deformable surface given correspondences with a reference image into a w ...

2012

Surface second harmonic generation from coumarin 343 dye-attached TiO2 nanoparticles at liquid-liquid interface

Hubert Girault

The nonlinear optical properties of coumarin 343 (C343) dye-attached TiO2 nanoparticles in the size range 5-8 nm adsorbed at the interface of water/1,2-dichloroethane have been studied by using the surface second harmonic generation technique. No second ha ...

Springer Verlag2011