arXiv subjects

Thilo M. Simon

Publications and source records attributed to Thilo M. Simon.

3 recordsLinked to original sources

arXiv2019

Unraveling the role of dipolar versus Dzyaloshinskii-Moriya interaction in stabilizing compact magnetic skyrmions

Magnetic skyrmions have been the subject of extensive experimental studies in ferromagnetic thin films and multilayers, revealing a diversity in their size, stability and internal structure. While the orthodox skyrmion theory focuses on the Dzyaloshinskii-Moryia interaction (DMI) and neglects higher-order energy terms, it is becoming clear that the full stray field energy needs to be taken into account to understand these recent observations. Here we present a micromagnetic study based on rigorous mathematical analysis which allows to account for the full stray field energy in the thin film and low DMI regime. In this regime, the skyrmion profile is close to a Belavin-Polyakov profile, which yields analytical expressions for the equilibrium skyrmion radius and energy. The obtained formulas provide a clear identification of Dzyaloshinskii-Moryia and long-range dipolar interactions as two physical mechanisms determining skyrmion size and stability, a consideration of importance for the optimization of skyrmion characteristics for spintronic applications.

cond-mat.mtrl-sci↗

arXiv2018

Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via H-measures

We quantify the rigidity of branching microstructures in shape memory alloys undergoing cubic-to-tetragonal transformations in the geometrically linearized theory by making use of Tartar's H-measures. The main result is a $B^{2/3}_{1,\infty}$-estimate for the characteristic functions of twins, which heuristically suggests that the larger-scale interfaces can cluster on a set of Hausdorff-dimension $3-\frac{2}{3}$. We provide evidence indicating that the dimension is optimal. Furthermore, we get an essentially local lower bound for the blow-up behavior of the limiting energy density close to a habit plane.

math.AP↗

arXiv2017

Maximum palinstrophy amplification in the two-dimensional Navier-Stokes equations

We derive and assess the sharpness of analytic upper bounds for the instantaneous growth rate and finite-time amplification of palinstrophy in solutions of the two-dimensional incompressible Navier-Stokes equations. A family of optimal solenoidal fields parametrized by initial values for the Reynolds number $\textrm{Re}$ and palinstrophy $\mathcal{P}$ which maximize $d\mathcal{P}/dt$ is constructed by numerically solving suitable optimization problems for a wide range of $\textrm{Re}$ and $\mathcal{P}$, providing numerical evidence for the sharpness of the analytic estimate $d\mathcal{P}/dt \leq \left(a + b\sqrt{\ln\textrm{Re}+c} \, \right) \mathcal{P}^{3/2}$ with respect to both $\textrm{Re}$ and $\mathcal{P}$. This family of instantaneously optimal fields is then used as initial data in fully resolved direct numerical simulations and the time evolution of different relevant norms is carefully monitored as the palinstrophy is transiently amplified before decaying. The peak values of the palinstrophy produced by these initial data, i.e., $\sup_{t > 0} \mathcal{P} (t)$, are observed to scale with the magnitude of the initial palinstrophy $\mathcal{P}(0)$ in accord with the corresponding $\textit{a priori}$ estimate. Implications of these findings for the question of finite-time singularity formation in the three-dimensional incompressible Navier-Stokes equation are discussed.

physics.flu-dyn↗