arXiv subjects

Matthias Ruf

Publications and source records attributed to Matthias Ruf.

24 records · Page 2Linked to original sources

arXiv2017

Motion of discrete interfaces in low-contrast random environments

We study the asymptotic behavior of a discrete-in-time minimizing movement scheme for square lattice interfaces when both the lattice spacing and the time step vanish. The motion is assumed to be driven by minimization of a weighted random perimeter functional with an additional deterministic dissipation term. We consider rectangular initial sets and lower order random perturbations of the perimeter functional. In case of stationary, $α$-mixing perturbations we prove a stochastic homogenization result for the interface velocity. We also provide an example which indicates that stationary, ergodic perturbations do not yield a spatially homogenized limit velocity for this minimizing movement scheme.

math.AP↗

arXiv2016

Continuum limit and stochastic homogenization of discrete ferromagnetic thin films

We study the discrete-to-continuum limit of ferromagnetic spin systems when the lattice spacing tends to zero. We assume that the atoms are part of a (maybe) non-periodic lattice close to a flat set in a lower dimensional space, typically a plate in three dimensions. Scaling the particle positions by a small parameter $\varepsilon>0$ we perform a $Γ$-convergence analysis of properly rescaled interfacial-type energies. We show that, up to subsequences, the energies converge to a surface integral defined on partitions of the flat space. In the second part of the paper we address the issue of stochastic homogenization in the case of random stationary lattices. A finer dependence of the homogenized energy on the average thickness of the random lattice is analyzed for an example of magnetic thin system obtained by a random deposition mechanism.

math.AP↗

arXiv2016

On the continuity of functionals defined on partitions

We characterize the continuity of prototypical functionals acting on finite Caccioppoli partitions. In the spirit of the classical Reshetnyak continuity theorem for measures that can be used to prove continuity of surface-type functionals defined on single sets of finite perimeter we show that in the multiphase case continuity is equivalent to convergence of the perimeter of the jump set.

math.FA↗

arXiv2016

On global and local minimizers of prestrained thin elastic rods

We study the stable configurations of a thin three-dimensional weakly prestrained rod subject to a terminal load as the thickness of the section vanishes. By $Γ$-convergence we derive a one-dimensional limit theory and show that isolated local minimizers of the limit model can be approached by local minimizers of the three-dimensional model. In the case of isotropic materials and for two-layers prestrained three-dimensional models the limit energy further simplifies to that of a Kirchhoff rod-model of an intrinsically curved beam. In this case we study the limit theory and investigate global and/or local stability of straight and helical configurations. Through some simple simulations we finally compare our results with real experiments.

math.AP↗

arXiv2015

Chirality transitions in frustrated $S^{2}$-valued spin systems

We study the discrete-to-continuum limit of the helical XY $S^{2}$-spin system on the lattice $\mathbb{Z}^{2}$. We scale the interaction parameters in order to reduce the model to a spin chain in the vicinity of the Landau-Lifschitz point and we prove that at the same energy scaling under which the $S^{1}$-model presents scalar chirality transitions, the cost of every vectorial chirality transition is now zero. In addition we show that if the energy of the system is modified penalizing the distance of the $S^{2}$ field from a finite number of copies of $S^{1}$, it is still possible to prove the emergence of nontrivial (possibly trace dependent) chirality transitions.

math-ph↗

arXiv2008

Pair production in laser fields oscillating in space and time

The production of electron-positron pairs from vacuum by counterpropagating laser beams of linear polarization is calculated. In contrast to the usual approximate approach, the spatial dependence and magnetic component of the laser field are taken into account. We show that the latter strongly affects the creation process at high laser frequency: the production probability is reduced, the kinematics is fundamentally modified, the resonant Rabi-oscillation pattern is distorted and the resonance positions are shifted, multiplied and split.

physics.atom-ph↗