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Now showing items 21-30 of 110

#### On the energy of critical solutions of the binormal flow

(2020-07-02)

The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisenberg model in ferromagnetism, and the 1-D cubic ...

#### 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 ...

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

(2020-06-01)

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

#### 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 ...

#### Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation

(2020-05-01)

We give the asymptotics of the Fourier transform of self-similar solutions for the modified Korteweg-de Vries equation. In the defocussing case, the self-similar profiles are solutions to the Painlevé II equation; although ...

#### 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 ...

#### Uniqueness properties of solutions to the Benjamin-Ono equation and related models

(2020-03-15)

We prove that if u1,u2 are real solutions of the Benjamin-Ono equation defined in (x,t)∈R×[0,T] which agree in an open set Ω⊂R×[0,T], then u1≡u2. We extend this uniqueness result to a general class of equations of Benjamin-Ono ...

#### 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. ...