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Now showing items 1-10 of 12

#### Invariant measures for the dnls equation

(2020-10-02)

We describe invariant measures associated to the integrals of motion of the periodic derivative nonlinear Schr\"odinger equation (DNLS) constructed in \cite{MR3518561, Genovese2018}. The construction works for small $L^2$ ...

#### The Schrödinger equation and Uncertainty Principles

(2020-09)

The main task of this thesis is the analysis of the initial data u0 of Schrödinger’s initial value problem in order to determine certain properties of its dynamical evolution.
First we consider the elliptic Schrödinger ...

#### A geometric and physical study of Riemann's non-differentiable function

(2020-07-08)

Riemann's non-differentiable function is a classic example of a continuous but almost nowhere differentiable function, whose analytic regularity has been widely studied since it was proposed in the second half of the 19th ...

#### Pseudospectral Methods for the Fractional Laplacian on R

(2020-07-02)

In this thesis, first, we propose a novel pseudospectral method to approximate accu- rately and efficiently the fractional Laplacian without using truncation. More pre- cisely, given a bounded regular function defined over ...

#### Exact Constructions in the (Non-linear) Planar Theory of Elasticity: From Elastic Crystals to Nematic Elastomers

(2020-07)

In this article we deduce necessary and sufficient conditions for the presence of “Conti-type”, highly symmetric, exactly stress-free constructions in the geometrically non-linear, planar n-well problem, generalising results ...

#### Vortex Filament Equation for some Regular Polygonal Curves

(2020-06-15)

One of the most interesting phenomena in fluid literature is the occurrence and evolution of vortex filaments. Some of their examples in the real world are smoke rings, whirlpools, and tornadoes. For an ideal fluid, there ...

#### Geometric differentiability of Riemann's non-differentiable function

(2020-06)

Riemann’s non-differentiable function is a classic example of a continuous function which is almost nowhere differentiable, and many results concerning its analytic regularity have been shown so far. However, it can also ...

#### Magnetic domain-twin boundary interactions in Ni-Mn-Ga

(2020-04)

The stress required for the propagation of twin boundaries in a sample with fine twins increases monotonically with ongoing deformation. In contrast, for samples with a single twin boundary, the stress exhibits a plateau ...

#### Evolution of Polygonal Lines by the Binormal Flow

(2020-02-05)

The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schr ̈odinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. ...

#### A sharp lorentz-invariant strichartz norm expansion for the cubic wave equation in \mathbb{R}^{1+3}

(2020)

We provide an asymptotic formula for the maximal Stri- chartz norm of small solutions to the cubic wave equation in Minkowski space. The leading coefficient is given by Foschi’s sharp constant for the linear Strichartz ...